{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T13:51:39Z","timestamp":1769003499104,"version":"3.49.0"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T00:00:00Z","timestamp":1736294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relationship between the solutions of these equations and their associated functions. Leveraging the symmetry between positive and negative solutions simplifies the derivation of criteria that ensure the oscillation of all solutions. Using precise techniques such as the Riccati method and comparison methods, innovative criteria are developed that guarantee the oscillation of all the solutions of the studied equations. The study provides new conditions and effective analytical tools that contribute to deepening the theoretical understanding and expanding the practical applications of these systems. Based on solid scientific foundations and previous studies, the research concludes with the presentation of examples that illustrate the practical impact of the results, highlighting the theoretical value of research in the field of neutral differential equations.<\/jats:p>","DOI":"10.3390\/sym17010087","type":"journal-article","created":{"date-parts":[[2025,1,8]],"date-time":"2025-01-08T09:30:45Z","timestamp":1736328645000},"page":"87","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Asymptotic and Oscillatory Properties for Even-Order Nonlinear Neutral Differential Equations with Damping Term"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2393-4418","authenticated-orcid":false,"given":"Belal","family":"Batiha","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science and Information Technology, Jadara University, Irbid 21110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2382-6553","authenticated-orcid":false,"given":"Nawa","family":"Alshammari","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"}]},{"given":"Faten","family":"Aldosari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Shaqra University, P.O. Box 15572, Shaqra 11961, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4643-8318","authenticated-orcid":false,"given":"Fahd","family":"Masood","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education and Science, University of Saba Region, Marib 14400, Yemen"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen"},{"name":"Jadara Research Center, Jadara University, Irbid 21110, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,8]]},"reference":[{"key":"ref_1","unstructured":"Norkin, S.B. (1965). Second Order Differential Equations with Retarded Argument, Nauk."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hale, J.K. (1977). 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